An In-Depth Analysis Approach Enabling Precision Single Chain Nanoparticle Design

The synthesis of single chain nanoparticles (SCNPs) is a vibrant field in macromolecular science, enabled by a rich variety of synthetic strategies to induce macromolecular chain folding. Due to the decrease of the hydrodynamic volume upon folding, SCNP formation is typically characterized by a shift towards higher elution volumes in size exclusion chromatography (SEC). However, a step-change in the methodologies for SCNP analysis is required for the in-depth understanding of the nature of intramolecular polymer folding and internal SCNP structure, which is critical to enable their application as catalytic nanoreactors. Herein, we exploit a unique combination of small-angle neutron scattering (SANS), 19 F NMR spectroscopy, and quadruple detection SEC to generate an encompassing and systematic view of the folded morphology of poly( tert -butyl acrylate) based-SCNPs as a function of their reactive group density (5, 15, and 30 mol%) and absolute molar mass (20, 50, 100 kDa). In addition to detailed morphological insights, we establish that the primary factor dictating the compaction of SCNPs is their reactive group density, which is ineffective below 5 mol%, reaching maximum compaction close to 30 mol%. The molar mass of the precursor polymers has a minor impact on how an SCNP compacts for molar masses above 20 kDa. These results are validated by the systematic combination of complementary scaling approaches using key parameters including molar mass, second virial coefficient, segment length, intrinsic viscosity, gyration, hydrodynamic and viscosity radii and apparent density. As an alternative to the apparent density, we introduce the contraction ratios g and g ´ as simple yet meaningful tools to compare SCNPs properties regardless of the synthetic strategy. Calculations of the scaling exponent as well as the complementary Kuhn-Mark-Houwink exponent unlock the highest achievable density for the 50 and 100kDa polymers leading to a hard sphere shape. However, the segment density based on generalized ratios of different radii and detailed Kratky and Casassa analysis of the SANS scattering behaviour unravel joint dense globular and linear segments within these SCNP structures.


Introduction
The precisely folded structure of biomacromolecules, such as proteins and enzymes, dictates their biochemical function. 1 Taking inspiration from nature, synthetic linear copolymers can be folded intramolecularly, forming dense single-chain nanoparticles (SCNPs). 2,3 The intramolecular crosslinking can be of static or dynamic, non-covalent or covalent nature. 4 The versatile molecular design of SCNPs allows for precise control over their architecture, 5,6 conformation and size, 7,8 rendering them ideal candidates for enzyme mimicry, 9 advanced catalysis, 10 drug delivery, 11 or targeted imaging. 12 Deducing generalized structure-property relationships for the size and conformation of SCNPs, regardless of the employed synthetic strategy, represents a fundamental step towards the advanced design of polymer nanoparticles, which is still lacking today. Yet, the essential requirement for the rational design of SCNP with properties close to the perfection of their natural counterparts is the fine control of the key parameters affecting SCNP formation. Thus, the precise analysis of the macromolecules before and after the folding process is critically required to establish complete understanding of these key parameters.
Analysis of the primary chemical structure of copolymers is conventionally carried out via 1 H and 13 C nuclear magnetic resonance (NMR) spectroscopy, while versatile NMR active nuclei enable monitoring the chemical transformations occurring during SCNP synthesis. A noteworthy illustration is a study that monitored the collapse of Pt II -SCNPs by phosphine ligand coordination using 31 P{ 1 H} NMR spectroscopy and corroborated via 195 Pt NMR measurements of the metal nuclei. 13 1 H and DOSY NMR measurements was used by our team to monitor step-wise unfolding of SCNPs by changes in chemical composition, and hydrodynamic size. 14 Furthermore, exploiting the high sensitivity of the 19 F nucleus, Perez-Baena et al.
studied successfully B(C6F5)3 catalyzed folding reactions. 15 Currently, size exclusion chromatography (SEC) is the most widely employed technique for mapping compaction during SCNP synthesis, as it separates molecules according to the hydrodynamic volume. The folding of SCNPs leads to a shift of the SEC trace towards higher elution volumes, relative to the starting material of the linear polymer ( Figure 1). 2 The assumption of relative size change is only valid under ideal SEC conditions, i.e. the separation occurs purely entropically and no enthalpic interaction with the columns occurs. 2 Meeting these requirements is non-trivial, as the folding reaction usually entails chemical transformation. Thus, if the precursor did not experience enthalpic interactions with the stationary phase, the SCNP might behave differently, and vice versa. If the delay of the elution volume relative to a linear precursor is caused by both column interaction and hydrodynamic compaction of the analyte, the results will be significantly skewed. The current limitation in monitoring the folding process of SCNPs relies on using SEC with simple differential refractometry (dRI) detection and calculation of sizes based on SEC standards. Even detection of absolute molar masses using multi-angle static light scattering (MALS) in SEC-dRI-MALS can be strongly limited due to the small sizes of SCNP structures. 16 In order to gain deeper insight into the nature of SCNP folding, advanced hyphenated techniques such as hyphenating SEC-dRI-MALS systems to viscometry, fluorescence, or UV/Vis detectors are critically required. SEC-dRI-MALS enables the study of the molecular conformation of polymers and their apparent density, as well as revealing undesired multichain aggregation. 17,18 Evaluation of the conformation via MALS requires a certain molar mass range (spanning at least two orders of magnitude), making narrowly distributed polymer samples difficult to analyze. 2 In the case of isotropic scattering (SCNPs below 10 nm in diameter), or samples with a low optical contrast, the fundamental evaluation of the radius of gyration (Rg) and the absolute weight average molar mass Mw becomes impossible via MALS. Quasi-elastic light scattering (QELS, known also as dynamic light scattering) can determine the hydrodynamic radius (Rh) of particles down to only a few nm, providing information on the segmental density and shape of the separated particles via the ratio = Rg/Rh. 2 As aggregation or broad distributions lead to a drastic overestimation of the Rh, QELS ideally should be coupled to a size separation technique (such as SEC). Unfortunately, the downstream dilution after SEC is an obstacle that SEC-QELS characterization of SCNPs has not overcome to date. By measuring rheological properties in solution, online viscometry (VS) is truly orthogonal to the optical detectors (QELS, MALS, dRI), and therefore capable of analysing samples that isotropically scatter light, as well as samples with low optical contrast. The spatial compaction of SCNPs is indicated by a decrease in the intrinsic viscosity [], or the viscometric radius (Rη), respectively. [19][20][21][22][23][24][25] Viscosity data from SEC-dRI-MALS-VS experiments allows for the analysis of the solvent specific conformation of the polymer, providing valuable information about the macromolecular scaling or the solvent quality. Although limited techniques have been reported beyond SEC, complementary techniques to SEC separation such as mass spectrometry, 26 atomic force microscopy (AFM) 7,[27][28][29][30][31][32][33] or cryogenic transmission electron microscopy (Cryo-TEM) 21,34 enable detailed insights into the properties of SCNPs for appropriate materials.
Small-angle neutron scattering (SANS) provides unrivalled insights into soft matter materials. Due to the use of neutrons as the scattering source, SANS allows for non-destructive determination of the absolute radius of gyration (Rg) for particles between 1 nm -300 nm in size. 35 A lot of information can be obtained from SANS data by a model-independent analysis, where standard plotting approaches such a Holtzer, Kratky, and Porod plots are the most commonly used. Furthermore, a model-dependent analysis can be performed by fitting the SANS data to various form factor models, which aids in deducing critical information regarding the microstructure (e.g. shape, mass fractals or segment density, compactness, stiffness of the polymer backbone, etc.), as long as a sufficient contrast is manipulated, e.g. by using either a (partially) deuterated solvent or by deuteration of parts of the solute. 35 The disadvantages of SANS include high costs, the need for high sample quantity and purity, and extensive data-processing. However, its ability to provide characterisation in the sub 10 nm realm, which includes the majority of SCNPs, makes this an extremely powerful analytical tool. Initial neutron scattering characterization by Pomposo et al. provided insights into the shape and the compactness of SCNPs. 36 Other studies have applied Kratky plots to the scattering data of SCNPs to confirm the increase of intramolecular density. [36][37][38][39][40] Recently, a good prediction of experimentally observed relative chain collapses was set by a relation from a pool of literature values by invoking Flory-Fox theory. 41 Theoretical calculation and simulation frequently assist the interpretation of experimental characterization. 6,13,15,24,36,37,[42][43][44][45][46][47][48][49] Chain-dynamics and collapse processes have been assessed, mostly by semi-empirical and statistical approaches. 42 Not surprisingly, the complexity of macromolecular dynamics makes ab initio quantum chemical calculations less applicable for SCNPs. Limiting the range of temperature and polymer lengths, Danilov et al. presented an extensive thermodynamic characterization of a reversible selective point folding, spanning the opening and closing transition with atomistic models. 47 Importantly, Monte Carlo simulations enable the simultaneous tracing of the folding process. 50 Very recently, Sommer and co-workers revealed the underestimated impact of solvent conditions during the folding on the SCNP structure. 51,52 Fundamental progress towards understanding the structure-property relationships of SCNPs has thrived in the last 10 years. Nevertheless, an in-depth understanding of the correlation between the key parameters molar mass and folding group density to the resulting SCNP morphology is critically missing. Thus, advanced characterisation techniques need to be developed to facilitate the purposeful design of SCNP structures. Herein, we fill this critical gap based on a unique combination of analytical techniques. The investigated SCNPs are constructed from poly(pentafluorobenzyl-stat-tert-butyl acrylate) precursors spanning a defined range of reactive group density (5 to 30 mol% pentafluorobenzyl acrylate) and molar masses (20 to 100 kDa), and the resulting morphologies are investigated by a fusion of small-angle neutron scattering (SANS), 19 F NMR spectroscopy and quadruple size-exclusion chromatography (SEC-RI-MALS-VS-QELS), coined SEC-D4. This combination of sophisticated techniques provides an unprecedented picture of both the outer as well as inner structure of compactly folded single chains to deduce general trends of structure property relationships for any SCNP material.

Results and Discussion
The SCNP folding strategy in the current work is based on the regioselective para-fluoro thiol reaction (PFTR), which allows for the folding of the polymer precursors using an external dithiol crosslinker 1,4benzenedimethanethiol (BDMT). Inspired by the work of Roth et al., we employed pentafluorobenzyl acrylate (PFBA) as a functional monomer to introduce pentafluorobenzyl (PFB) moieties for the selective nucleophilic aromatic substitution at the para fluorine atom along the precursor backbone. 53 Thiols exhibit increased acidity and nucleophilicity compared to amines or alcohols, allowing for less harsh reaction conditions for the regioselective PFTR reaction. 54 Importantly, 19 F NMR in combination with 1 H NMR spectroscopy facilitates the precise determination of the absolute SCNP composition, which we purposefully manipulated by molar mass and number of crosslinks of our defined precursor library ( Figure   2). Thus, we tune the morphology of the SCNPs by both the systematic variation of the primary structure of precursor chains (repeat-unit folding approach), and of versatile length by a folding strategy in a poor solvent. 55

Linear Precursors
The functional monomer pentafluorobenzyl acrylate (PFBA) was synthesized in a one-pot procedure described in the Supporting Information (SI, section 3.3). 53 The chain transfer agent cyanomethyl dodecyl trithiocarbonate (CMDT) facilitated the reversible addition-fragmentation chain transfer (RAFT) polymerization of the functional monomer pentafluorobenzyl acrylate (PFBA) and tert-butyl acrylate ( t BuA). 56 Herein, three chain lengths of linear precursors with targeted molar masses of 20, 50, and 100 kDa were obtained. As depicted in Figure 2, each molar mass was synthesized for three different PFBA monomer contents ranging from low (approximately 5%, colored green, A samples) to mid (approximately 15%, colored blue, B samples) to high (approximately 30%, colored black, C samples) feed ratios, randomly distributed per chain. As the amount of PFBA incorporation into the precursor backbone is in-line with the targeted values, the precursor library is suited for the fine-tuning of the ligation-density in the subsequent folding reaction.  Initial SCNP folding of the RAFT-based precursors proved difficult due to the sulfur end groups, therefore, we employed a radical-induced oxidation in a facile one-pot procedure as described by Barner-Kowollik and coworkers in order to remove the terminal trithiocarbonate moieties. [57][58][59][60] The optimization of the conditions of end group removal was performed on representative copolymers as described in the Supporting Information (section 3.4). The success of RAFT group removal was confirmed by 1 H NMR spectroscopy on smaller copolymers as evidenced by the disappearance of the C(S)SCH2 signal at 3.25 ppm (section 3.4.2, SI- Figure 12). 60,61 The quantification of the polymer composition was performed for both the parent RAFT copolymer, and for the precursor after trithiocarbonate group removal via 1 H NMR spectroscopy with only negligible deviation observed.
The composition of the polymer (comonomer ratio and crosslinker content for the SCNPs) per chain directly impacts the optical properties of the copolymers (refractive index, dn/dc, the extinction coefficient, etc.) and all concentration dependent measures, respectively. The determination of the optical contrast dn/dc is critical for accurate molar mass determination using light scattering techniques and was determined for all precursors and the SCNPs. We employed a calculation procedure allowing to deduce reliable refractive index increments (Table 1) for any composition of the precursors as well as of the SCNPs (refer to section 3.2 of the SI).

Single Chain Nanoparticles (SCNPs)
The primary structure of the precursor was designed to enable a systematic variation in the final size and conformation of the SCNPs. The mol% of PFB in the precursor polymers defines the reactive group density and therefore fine-tunes the number of crosslinks in the folding reaction. All crosslinkable moieties of the precursor as well as the procedure for the evaluation of the absolute SCNP composition, are depicted in  Poor solvent conditions during the folding reaction, enabling the densest possible conformation of the linear precursor, are critical to generate compact SCNPs, as was demonstrated by Sommer et al. 51 Optimal solubility of the precursor library was observed in polar solvents (i.e. poor solubility, below thetaconditions), facilitating a more densely packed random coil of the precursor polymer, thereby leading to a more tightly intramolecularly folded SCNP. Thus, the polar aprotic solvent acetonitrile (ACN) was ideal for the intramolecular folding process.
The external crosslinker 1,4-benzenedimethanethiol (BDMT) was added equimolarly with respect to the functional PFB groups of the precursor (refer to the SI, section 3.5). The use of an external crosslinker is analogous to substrate binding for enzyme activitya diffusion governed process -thus a higher than stoichiometric amount of external crosslinker is required for successful intramolecular folding. 62 Polar solvents not only facilitate the PFTR, but also the disulfide formation -a parasitic side reaction in this instance. 63 To overcome this issue, a catalytic amount of dimethylphenylphoshine (DMPP) is utilized as a reducing agent to effectively avoid disulfide-linkage of the crosslinker. 64,65 This parasitic side reaction would otherwise lead to decreased PFTR turnover and intermolecular ligation.
The successful generation of a structural hierarchy towards SCNPs, based on PFTR using an external crosslinker, required comprehensive optimization until a facile one-pot procedure was established (SI, section 3.5.1). Small additions of a good solvent (tetrahydrofuran, THF) was found to assist the PFTR reaction, whilst maintaining poor solvent conditions for the macromolecules. THF was added dropwise, under stirring, as the reaction rate of PFTR is rather slow in THF, 63 until the solution became transparent.
The required amount of good solvent was found to depend on the molar mass and on the amount of PFB incorporation. A clear dependence of the solvent quality with increasing PFB concentration (5% PFB (A) > 15 % PFB (B) > 30% PFB (C)) in the polymer backbone of the precursor was observed. Highly PFB decorated precursors are less soluble because of the highly polar C-F bonds, which can alter the overall polarizability and solubility of highly fluorinated polymers. [66][67][68] Excess of the base triethylamine (TEA) served not only to further solubilize the precursor, but also mitigated competitive behavior between the hydroxy endgroup of the precursor and the thiol-groups of the external crosslinker. 53,[69][70][71] Attempts to increase the reaction rate by a stronger base were not successful. 54,[70][71][72][73] To compensate for the use of TEA and the dilution required for SCNP synthesis, long reaction times are required. 63 The long reaction time is also intended to compensate for the increasing rigidity of the polymer as intramolecular ligation increases, and the decreasing of available PFB moieties. 29 The folding reaction was quenched by scavenging the unreacted thiols via a Michael reaction with methylacrylate (MA), successfully avoiding intermolecular side reactions or column interaction during SEC characterization. 63 The reaction times allowed the crosslinker molecules to reach even sparsely functionalized precursors in order to transform them into SCNPs at room temperature. Near quantitative conversion of the PFTR reaction was observed for the PFB groups of the B and C precursors, whereas the side-groups of sparcely decorated A-samples (approximately 5% PFB) were transformed with approximately 50-60 % PFTR conversion only ( Figure 4). The lower reaction rate is in good correlation with the lower amount of reactive groups but additional reason is the more open precursor conformation, when compared to higher decorated samples of similar molar mass. 46 Thus, the composition and the conformation of the precursor during the folding reaction are influencing the probability of folding events and the intra-chain distances, respectively. 51

Composition of the SCNPs
The turnover of the intramolecular PFTR can be accurately quantified (refer to the SI, section 3.5.4) via highly sensitive 19 F NMR spectroscopy. The pentafluorobenzyl moiety shows three distinct signals of the ortho-, meta-, and para-fluorine atoms as depicted in Figure 3 (refer to the SI, section 3.5.4). 53 Whereas the integration of all signals (Fo, Fm, Fp) enables the accurate quantification for small molecule experiments, only the signal integrals of the meta-flourine atoms in the precursor (Fm) and in the reacted PFB moiety (Fm') can be used to quantify the average conversion of the PFTR for polymers by To quantify the ligation events, we use the term of ligation density (LD). The LD is the number of crosslinking events of the functional side groups with respect to the degree of the polymerization of the precursor chain. When comparing different chain lengths, the relative value of the LD is a useful measure. Figure 3 shows that the amount of substituted para-fluoro atoms is a product of the PFTR-conversion χPFTR (determined via 19 F NMR spectroscopy) and the molar amount of PFB units in the precursor´s backbone (determined by 1 H NMR spectroscopy).
Strictly speaking, crosslinking events cannot be derived from 19  Thus, the obtained library of precursor-SCNP pairs serves well to deduce structure-property relationships with regard to the chain lengths and the amount of crosslinker units per chain (Table 1). The library is thus key for elucidation the size and conformation of the precursor and their corresponding SCNPs by SEC-D4 and SANS characterization.

Molar mass, size and conformation via advanced size exclusion chromatography
State-of-the-art SEC-D4 characterization enables a comprehensive analysis of the precursor library and their folded counterparts. The successful interpretation of the SEC-D4 experiments depends on the precise determination of dn/dc (Eqs. SI-2 and SI-3), which is challenging in case of copolymers with composition variation. Very low optical contrast was observed for the precursor library in THF (dn/dc approx. 0.05 mL/g, see Table 1). Such an observation is somewhat expected due to the highly polar C-F bonds decreasing the overall polarizability of multi-fluorinated organic molecules, thus, influencing the refractive index increment dn/dc. [66][67][68] In contrast, sulphur belongs to the group of highly polarizable main group elements and the C-S bond has low polarity. 74 Therefore, the refractive index of the SCNPs is significantly increased due to incorporation of the dithiol-crosslinker. A comprehensive strategy for reliable evaluation of dn/dc dependent on the varied copolymer composition for both precursor and SCNPs is provided in the SI section 3.2. The exact knowledge of dn/dc is critically needed for samples of non-quantitative mass-recovery during SEC separation, which by definition limits the precise online determination of the dn/dc. Quantitative massrecovery in SEC separation for all precursors and most SCNPs (SI Table 8) allowed for reliable SEC interpretation and comprehensive online analysis of the dn/dc values of the complete library. well as for the SCNPs. The small high molar mass shoulder in some chromatograms is most probably caused by backbiting as a side reaction. 75,76 This shoulder disappears after folding due to further precipitation procedures. Table 1 shows that the overall polydispersity Đ is not significantly altered after the folding, indicating that the purification after the folding compensates for the generally expected increase of polydispersity during the folding process. 77 The shift of the peak from the precursor to the corresponding SCNP reveals the apparent decrease of the hydrodynamic size, which is more pronounced for higher LDs of the SCNPs. This observation is directly supported by the change of the intrinsic viscosity from the precursor to the corresponding SCNP ( Figure 5a). Figure 5b indicates the direct correlation between the extent of apparent hydrodynamic collapse by the peak apex shift along the elution volume axis (Ve) to the number of crosslinks per chain for all samples. Comparing the samples with similar LD (Figure 5c), it is obvious that the apparent hydrodynamic collapse is more significant for longer chains, because they possess larger number of segments, which increases the freedom for stronger conformational changes as discussed below.
Unfortunately, the determination of Rg is limited for particle sizes smaller than /20 nm (with  the wavelength of the incident beam) because of the lack of angular dependence of their scattering intensity (isotropic scattering). With size ranges of below 12 nm, the SCNPs fall within the isotropic scattering regime. Even though, the reproducibility of the triple determination of the Rg values for the 50 kDa-, and the 100 kDa samples is high (SI Table 8 (Figure 5a and Table 1) clearly correlates to the theoretical amount of incorporated crosslinker (C > B > A), confirming the success of the folding reaction.
As discussed in the introduction, QELS is a complementary approach to MALS for determination of small polymers down to several nm. Therefore, part of the SEC-D4 equipment was a QELS-detector for the determination of the hydrodynamic radius Rh. According to the Stokes-Einstein equation (Eq. SI-6) Rh corresponds to the radius of a hypothetical sphere which possesses the same diffusion coefficient as the measured macromolecule. Rh was frequently used for investigation of SCNPs using QELS in batch. 15,[78][79][80] Yet, the scattering intensity is proportional to the radius to the 6 th power, leading to overestimation of the radii whenever impurities (dust or broad distributions) are present in the sample. The limited precision of QELS-batch characterization was analysed by our team, noting that it can lead to strong deviation from reality. 80 Consequently, QELS detection is most effective when coupled to a size separation, as each elution fraction can be considered monodisperse. 18 Unfortunately, poor signal-to-noise ratio is a well-known obstacle due to dilution in the SEC column additionally to the low optical contrast dn/dc. Therefore, only the Rh from samples with sufficiently high dn/dc (SCNP with high crosslinker incorporation) were successfully characterized via online-QELS technique and are listed in SI Table 9. In conclusion, due to the limits of the light scattering, the reliable analysis of Rg and Rh was not possible over the complete range of samples' library via SEC-D4.
Online viscometry is orthogonal to all previously described detectors, as it measures rheological properties in solution and is independent of their optical features. In contrast to the results from MALS and QELS detectors, the signal of the viscometer shows excellent signal-to-noise ratio -even for particle sizes below the size-limit of light scattering. The spatial compaction of SCNPs should lead to a decrease in intrinsic viscosity [η] which in turn is correlating with a decrease in the viscometric radius, Rη, according to Eq. (4).
[ ] = 10 3 The SCNPs of all molar mass ranges clearly follow the expected trend that increasing number of crosslinks per chain lead to increasing chain collapse of the SCNPs and confirm the volume reduction found by the shift of Ve (Figure 5b,c).
In contrast to the 50 kDa and 100 kDa samples, we obtain atypical results for the smallest (20 kDa) samples ( Figure 6b). Sample 20A shows a slight increase of R, in contrast to the expected decrease as found for 20C. This unexpected result is unlikely associated with experimental error as the triple determination of R for all 18 samples shows not only a low uncertainty for each experiment, but is also reproducible for each sample (SI Table 9). Nevertheless, it is not possible to suggest a lower physical limit for small particle size of this technique, as it strongly depends on the pressure, the temperature and the set-up.
We hypothesize that the short chain length is to be the reason for the atypical size development of the 20 kDa samples resulting in smaller volume reduction compared to larger precursor chains. Only short distance interactions (i.e. more local crosslinking as opposed to end-to-end crosslinking) are possible in shorter chains, while longer chains have greater potential for long-distance interactions between the macromolecular segments. This is justified with the small number of segments at a fixed persistence length.  Of course, such behaviour depends on the number of crosslinks per segment which is reflected in the relative numbers of crosslinks per precursor chain (or LD in %). The trend of increasing compaction is similar for all molar mass series (see Figure 5c). However, the effect of the absolute amount of crosslinks per chain seems to be the driving parameter of the folding behavoiur and is depending on the contour length of the chains. Furthermore, having a particular composition and thus, particular persistence length of the macromolecule implies an increasing number of the segments (increasing molar mass) will lead to increasing number of long-distance interactions between the segments for long chains. In contrast, predominantly short distance interactions occur for shorter chains, which may rather occur along the chain (2D contraction) than over intra-chain space (3D contraction, according to the classical understanding of folding). Further experimental confirmation of other repeat unit folding SCNP-systems is beneficial to validate this hypothesis of the interplay between chain-length and folding conditions.
Information on the compactness of polymer chains is obtained by the molar mass dependence of the intrinsic viscosity according to the Kuhn-Mark-Houwink (KMH) plot, which by theory correlates with the [ ] = The average KMH-slopes of all samples are given in Table 1 and in Figure 8. All precursors show KMHslopes above 0.5, corresponding to a polymer coil in good solvent conditions. 35 Lower values indicate a more compact structure for the corresponding SCNPs. The SCNPs of the lowest LD (A-samples) show no significant change of compactness, as the KMH-slope only changes marginally. In contrast, the compactness of the B-samples is significantly higher due to intramolecular ligation. Accordingly, the tightly crosslinked C-samples adopt a mostly compact spherical conformation (close to  = 0 for solid sphere). In contrast to the clear impact of the LD on the KMH slope, the molar mass does not show significant influence on the conformation (Figure 8b).

Figure 8. (a) KMH plots of the precursors (open dots) and their corresponding SCNPs (full dots) of 50 kDa series. (b) KMH exponents of the whole copolymer library depending on the crosslinks per chain. Data for precursors (open dots) and SCNPs (full dots)are presented. Limits for statistical coil and hard sphere are indicated in the plot and in the table within the figure. (c) Correlation between loop-length (stars) calculated from the LD and polymerisation degree vs SCNP conformation according to KMH slope (dots).
The knowledge about the number of crosslinks per chain provides insight into the average number of monomer units per loop, a suitable value to estimate the compactness of SCNPs. For simplicity, we can assume that the number of incorporated crosslinker units is equal to the average number of loops per chain. technique not limited to the approximate 10 nm size regime or optical contrast issues is required. We have therefore employed the powerful SANS technique to sharpen our understanding of these nanoobjects.

In-depth size and conformation validation via SANS
SANS is unrivalled in analytical power for soft matter materials, as it provides the non-destructive determination of the absolute Rg for particles down to 1 nm in size and additionally provides the information about the microstructure (shape and segment density) of the analyte. 82 Figure 9a shows an example of a scattering curve of the 50C-pair of precursor and SCNP and the ranges of the scattering curve delivering information about size (Rg), conformation (scaling exponent  in Eq. 3) and flexibility (segment length or Kuhn length lK) of the polymer chain (all scattering curves and their interpretation are given in SI, section 6). As the concentrations of the samples are held sufficiently below chain overlap concentration c* (SI, section 1), interparticle interaction is ruled out, 85 as confirmed by the absence of a structure factor peak. Therefore, we can focus on the form factor P(q) (SI, section 6.1) to investigate the scattering function of a single isolated polymer particle, revealing information about size and shape of the precursors and the corresponding SCNPs.
Using the Zimm analysis, the absolute Rg and the second virial coefficients A2 in THF-d8 were determined and are summarized in Table 1. Absolute particle sizes between 3 and 17 nm radius of gyration are obtained.
Good agreement with the tendencies found for R was found (Table 1, Figure 6). Furthermore, good correlation of the Rg values with the calculated molar masses from SEC-D4 is observed: already small changes of chain length for the 50 kDa precursor demonstrate an impact on the Rg (samples 50A, 50B, 50C in Table 1). The extent of collapse from precursor to SCNP is in direct relation to the extent of LD and correlates with the development of the size reduction calculated from the SEC-D4. Figure 9b shows the relative volume reduction Vg in comparison to the values calculated from the intrinsic viscosity V. The relative volume contraction is clearly dictated by the amount of crosslinks per chain. More precisely, Figure   9b reveals an asymptotic increase towards a maximum relative volume contraction of approx. 80 % with increasing ligation density after which a plateau is reached. These results confirm the results obtained from SEC-D4 and demonstrate that precise size-tuning of SCNPs is predominantly controlled by adjusting the precursor LD.
Having reliable information about the size reduction of the SCNPs after folding, which is confirmed by two independent analytical tools, SEC-D4 and SANS, the next logical step is to validate the reliability of the

(g) k-parameter, a generalised ratio between Rg (from SANS) and R (from SEC-D4), gives an insight into the segmental distribution and shape of the particles (see scheme) depending on the ligation density (precursorsopen; SCNPs -full symbols).
Further information from the Zimm analysis of the SANS results at low q-values delivers the second osmotic virial coefficient A2, which is a quantitative measure of the strength of interaction between the macromolecular segments. Good solvent conditions will lead to positive A2 values, whereas A2 = 0 corresponds to unperturbed dimensions of the macromolecules under theta-conditions. The obtained second virial coefficients in THF (Table 1) are similar for most precursors indicating good solvent conditions and decreasing to theta-conditions with increasing molar mass as expected. 35 Clear dependency of the A2 from the copolymer composition is observed for the 50 kDa samples (see Table 1). In accordance with the proposed hypothesis (Figure 7), the SCNPs show a negative A2 close to theta-state corresponding to the adjusted and "frozen" compact conformation by folding in a poor solvent (ACN/THF).
The compact conformation of the folded SCNPs and conformation of their precursors is impressively reflected in their different scattering behaviour. Figure 9a depicts the representative chain collapse of sample 50C visible in the significantly faster decay of the scattering intensity of the SCNPs compared to the precursor. The evaluation of the negative, reciprocal slope of the scattering curves delivers information on the fractal dimension, e.g. the scaling exponent , which describes the relation between the Rg and the molar mass of the macromolecules (Eq. 3). Additional fit to model form factors (polymer excluded volume) of the scattering curves P(q) was used to validate the evaluated values of the Rg from Zimm analysis and  from the slope of P(q). 86 The results from these fits show very good agreement with the manually evaluated data (see SI Table 10 and section 6.3 in the SI). Figure 9d shows that the scaling exponents of the precursor correspond to linear Gaussian chain conformation, which is defined by ν = 0.6 in a good solvent. 87 Colmenero et al. recently emphasized the similarity of Gaussian chain conformation to the scaling behaviour of intrinsically disordered proteins (IDPs) defined by their biological task. 44 Comparing the precursor to their corresponding SCNPs, a clear trend of increasing compaction with increasing LD is confirmed. Maximal compaction approaching spherelike conformation ( = 0.33) is obtained for the SCNPs of the C-series of the strongly crosslinked 50 and 100 kDa samples, while the 20 kDa sample show still pronounced but smaller compaction. This strong contraction is in full agreement with the slightly negative A2 values found in a good solvent (THF-d8), which can only be explained by the folding strategy under carefully chosen poor solvent conditions (see Figure 7). Furthermore, the analysis of the C-series shows convincingly that the conformation changes during folding are not only depending on the frequency of the crosslinking events (LD). Having maximum reduction of the SCNP volume (at 30% LD, Figure 9b) there is still room to control the final conformation from slightly compact chain conformation (20C) to sphere like (50C) to hard sphere (100C) by adjusting the absolute number of crosslinks, e.g. chain length.
The orthogonal analytical tools in this study allow for a unique comparison between the scaling exponent  and the KMH exponent both obtained in the same solvent conditions (THF for SEC-D4 and THF-d8 for SANS). Figure 9d further shows the values relation to the  values, which has its origin in the Flory mean-field theory as = (1 + ) / 3. 11,87,88  (C-samples). Our team earlier suggested that the minimum SCNP density is 0.1 g cm -3 , despite observing a large number of SCNP systems below this density threshold. The highest found dapp = 0.25 g cm -3 for our SCNPs is far below the 1 g cm -3 expected for bulk materials, which surprisingly, was reported for some SCNPs. 80 It should be noted that, the swelling behaviour in a good solvent as well as bulky functional groups within the SCNP structure could strongly influence the apparent density.
The change of density upon folding increases steadily with LD ( Figure 9e). The highest density is observed for the smallest SCNP sample f20C, but peculiarly, the change of density due to the folding is only changed to an extent comparable to the medium crosslinked SCNPs. In order to understand this effect more precisely, the density distribution within the macromolecule should be analysed. For this purpose, the generalised ratios kR/Rg) andRg/Rhcan be used asquantitative indicators of the molecular topology of polymers in solution. 18,89 kindicates the mass distribution around the centre of gravity and the hydrodynamic draining of the solvent, thus giving information about the segmental density in complex macromolecules. Figure 9g presents the kvalues of the samples investigated by SANS and SEC-D4. The topology of the precursors corresponds to the density-distribution of a linear coil (k = 0.6). The increase of kis minimal for the weakly crosslinked SCNPs (A-samples), and significant for the compact SCNPs (Csamples). As a reference, the theoretical maximum compaction of solid spheres has the ratio of k= 1.3. 90 The SCNP sample f20C has the highest mass-centred compactness. These results are confirmed by the complementary ρ-parameter based on the calculation of the Rh from SEC-D4 in combination with Rg form SANS (SI, section 4.3.2). The observation of the 20C sample behaviour coincides with the phenomena observed for the viscometric radii and the apparent density of the smallest polymers. We explain this phenomena by two main reasons: 80 (i) as discussed previously, shorter chains undergo predominantly short distance interactions under the poor solvent conditions due to limited number of segments able to form a loop over longer distances. Taking into account that the stiffness of the macromolecular chain is defined by the segment length, low number of segments does not allow a significant contraction in 3D sense, and the volume of the polymer coils is not significantly changed due to the folding reaction; (ii) at the same time, the mass-increase due to the incorporation of the external crosslinker contributes proportionally to the apparent density dapp (Eq. 6). Visualisation of the impact of mass increase on the density upon folding for small molar mass precursors is given in the SI, section 7.4.
The reduction of macromolecular size due to conformational changes is a well-known key issue in the branching theory, where the concept of contraction factors g and g´ is applied. 35,91,92 The contraction factors indicate the relative change of the main structure parameters used in this study, [] (viscosity model) and the Rg (radius model). We define the contraction factor as the ratio of the intrinsic viscosities of the precursor and the corresponding SCNP for a given DP (Eqs. 7 and 8). 35,88 The original introduction of contraction factors within the branching theory takes into account changes in [] or Rg at equal molar mass of a linear polymer an the branched analogue. In our study, we translate this relationship for SCNPs contraction at similar polymerisation degrees because of the increase of the molar mass of the precursor after folding. The SANS scattering curves of our library contain much more information than only the structural parameters discussed above. The extraction of this information can be performed by analysis of the scattering intensity P(q) according to Kratky or Casassa. 84,93,94 Kratky and Casassa plots can qualitatively assess the degree of folding and are suitable for determination of the flexibility of linear chains using the high q-regime (see Figure 9a). This analysis is usually applied to concentration dependent scattering curves, which leads to simplified data analysis. Although, Hawker et al. demonstrated in early SCNP research, that no remarkable differences of Kratky plots are given for different concentrations for slightly branched polystyrene-based SCNPs, 40 we plot the form factor P(q) corrected for angle and concentration dependency for sake of accuracy as obtained by our Zimm analysis.
Kratky plots of the dimension q 2 P(q) vs. q facilitate to decipher the segment density, as a plateau appears for polymers of a Gaussian coil conformation (q -2 -slope). In contrast, globular structures show a bell-shaped peak ( Figure 10c). 95,96 Kratky plots have been frequently applied to reveal the folding state of proteins, by referring the area of the bell above the plateau to the degree of folding. 95 This calculation approach can therefore, semi-qualitatively assess the degree of intramolecular ligation, as the position of the local maximum refers to the linear mass fractions of the particles. 93 SCNPs and intrinsically disordered proteins to that of compact globular proteins. 36 Instead, we compare the Kratky plots within a chemically similar system (e.g. precursor and the correlated SCNPs, or SCNPs of the same building blocks) to elucidate the density and sphericity of the polymers of our polymer library ( Figure   10). For all precursors, a plateau in a Kratky plot is obtained, resembling a Gaussian coil conformation (see SI, section 6). Increasing plateau height is, amongst other factors, caused by the different particle sizes (molar mass), which can be shown in a dimensionless Kratky plot (qRg) 2 P(q) vs. qRg, see SI, section 6.1.2).
Dimensionless Kratky plots have been, for example, applied to synthetic SCNPs, intrinsically disordered proteins and globular proteins by Pomposo et al. 36 In Figure 10a the 50 kDa series of the precursors are shown. Figure 10b shows the Kratky plots of the 50kDa SCNPs (all plots available in SI, section 6). In contrast to the less crosslinked SCNPs (A-samples), the strongly crosslinked SCNPs (B-and C-samples) show a pronounced Gaussian distribution in the Kratky plot indicating globular particles as also reported for globular proteins. 95 These local maxima of the Kratky plot indicate an increased segment density. The position of the apex of the peak (in q-dimension) is related to the size of the mass-fractals and resembles the trends observed for Rg of the SCNPs (Table 1). Contrary to the classical Kratky plots of spheres, a plateau is still present for the compact B-and C-series of the SCNPs at high q-values. This observation indicates the coexistence of multiple domains composed of dense-fractions and linear chain conformations also observed for proteins, 97 leading to the assumption that the macromolecule does not possess homogenous segment distribution, but linear segments and dense segments jointly exist. 93,96 The denser segmented regions in the SCNP structures can be described as cross-linking crowded regions however, this assumption needs further elucidation using theoretical consideration in future studies. Closer look at the 20C SCNPs (Figure 10b) shows that such a plateau is less pronounced for this small molar mass sample. This observation, analysed in the context of the calculated high apparent density and high segment density found for this particular sample (Figure 9e and 9g), confirms low amounts of linear segments but rather dense structure with small dimensions. These findings support the above discussed hypothesis of short distance interactions responsible for crosslinking at low degrees of polymerisation, which cannot lead to joined linear and dense, globular segments in one SCNP as in the case of the 50 and 100 kDa samples.
Similar to the Kratky plots, the Casassa plots of the SCNPs show a significantly increased maximum at low q-ranges (SI, section 6), which is typical for dense coil-structures. We apply this plot to deduce semiquantitative information about the coil behaviour itself, as the height of the maximum increases with decreasing deformability. The transition (denoted with q* in SI, section 6.1.3) from coil-like (low q-range) to rod-like behaviour (high q-range) enables the calculation of the segment length. Another way to calculate the segment length is using a fit with model form factors as described in the SI, section 6.3.1. leading to precise analysis of the particle's features. The form factor model flexible cylinder provides the ability to determine the Kuhn length lK, based on simulations of a discrete representation of a worm-like chain model of Kratky and Porod and normalized by the volume of a flexible cylinder. 98 For this purpose the SasView 86 application was used, as described in the SI, section 6. Very good fit quality was achieved for all precursor samples and assures high reliability of the obtained data. The obtained Kuhn lengths of the precursors between 3.2 and 4.2 nm are slightly lower than the approx. 4.6 nm found for poly( t Bu acrylate). 83 The shortest lK, thus, the most flexible chain, is found for the precursor 20C, whereas sample 50C shows the longest lK -although both precursors exhibit a comparable backbone composition. Generally, the A-samples show better flexibility, thus, the low crosslinking turnover of the low functionalized precursor is not caused by steric hindrance of potentially stiff backbone features, but is solely caused by statistically reduced intramolecular ligation events. Focusing on the 50kDa samples, a clear increase of lK is indicated, which correlates well with the decreasing solubility in the order A > B > C. From these reasons, we assume maximal flexibility of the polymer chain of A-precursors. The solvent quality and the chain stiffness, both in means of the degree of rotational freedom, are of paramount importance for the efficacy of the folding reaction. 99,100 As the bending stiffness of the linear precursor determines the probability of intramolecular interaction in space, and therefore influences the morphology of the SCNPs, we conclude negligible influence of changing backbone composition or stiffness on the SCNP morphology.

Conclusions
Regioselective para-fluoro thiol cross-linking allows for the precise design of a polymer library and its systematic folding into SCNPs defined by predetermined numbers of linkage points and molar masses.
Thus, two general properties of the precursor structure are investigated regarding their impacts on the SCNPs properties, making findings applicable to SCNPs regardless of the employed chemical strategy of the folding reaction.
Extensive 1 H NMR spectroscopy, 19 F NMR spectroscopy, SEC-D4 and SANS provide unique insight into the parameters limiting the formation of SCNPs. We combine these orthogonal instruments of advanced polymer analysis to obtain a multidimensional picture of the resulting architectures -from the chemical structure to the segment distribution to the global conformation.
The turnover of the crosslinking reaction and resulting size reduction of the formed SCNPs relative to the linear precursors directly correlates with two main parameters: the ligation density and the conformation of the linear precursor under the conditions of the folding reaction.
Based on molar masses from 20 to 100 kDa and ligation densities from 3 to 30% of the precursors, we estimate (i) a lower limit of 5% ligation density for effective crosslinking with minimum size reduction during SCNP formation and (ii) a higher limit of 30% ligation density leading to maximum achievable size reduction of 80%. These limits are additionally influenced by the molar mass of the precursor. For molar masses of 20 kDa, 80% volume contraction is not achievable due to lack of long-distance interactions as a result of low number of segments, which enable limited variation of the conformation even under poor solvent conditions.
In the molar mass range between 20 and 100 kDa, an effective control of the size reduction can be observed mainly depending on the absolute number of crosslinks per chain in the range between 5 and 40. These ranges are entirely independent on the chain length for molar masses above 20kDa. For more than 40 crosslinks at sufficiently high molar masses, no further increase of the compaction can be indicated.
These results are validated by the systematic combination of complementary scaling approaches using key parameters including molar mass, second virial coefficient, segment length, intrinsic viscosity, gyration, hydrodynamic and viscosity radii and apparent density. As an alternative to the apparent density, we introduce the contraction ratios g and g´ as simple yet meaningful tools to compare SCNPs properties regardless of the synthetic strategy. Calculations of the scaling exponent as well as the complementary Kuhn-Mark-Houwink exponent unlock the highest achievable density for the 50 and 100kDa polymers leading to a hard sphere shape. However, the segment density based on generalized ratios of different radii and detailed Kratky and Casassa analysis of the SANS scattering behaviour unravel joint dense globular and linear segments within these SCNP structures.
These fundamental insights into the parameters ruling the formation of SCNPs enable the precise assessment of the commonly used shift of the elution volume using SEC in comparison with multidetector SEC-D4 and profound validation of these results by SANS. While SEC-D4 has its limits in terms of the use of optical detectors due to very small SCNP sizes and low refractive index increment, it is a reliable technique for SCNP analysis, when viscosity detection is used. The accuracy of these experiments is, however, essentially dependent on precise absolute molar mass analysis using MALS detector and the careful determination of the refractive index increment.
The obtained results from SANS and SEC-D4 demonstrate that the shift of the elution volume, even if mainly entropic separation (according to particle size) is operational, cannot be used as a reliable detection of size reduction due to SCNP folding. The reasons of this limitation can be found in the changes of the chemical composition after folding as well as in the very complex conformation of the SCNP structures.
Further studies on the separation mechanisms in SEC should shed light on this question.
When exploring approaches for size tuned artificial nanocontainers, SCNPs represent an ideal avenue between synthetically demanding dendrimers and architectural delicate macro-complexes such as micelles or polymersomes. Exploiting the chemistry available for SCNP construction, we uncover general guidelines for the tailored design of SCNPs with regard to molar mass and number of linkable units for the precursor material. The introduced alternative parameters such as g, g', and k show better applicability than conventional ones such as the apparent density and size that are of generalized use for encapsulation, retention behaviour or for catalytic activities, and bring SCNPs applications within reach.