= Solution
The <coil-globule transition> is the contraction of an isolated flexible <polymer> as <solvent quality> worsens. A swollen chain in a <good solvent> has size $R\sim aN^{3/5}$ in the <Flory approximation>. At the <theta temperature> the effective two-segment <excluded volume> vanishes and $R\sim aN^{1/2}$. A <poor solvent> favors a dense <polymer globule>, with $R\propto N^{1/3}$ at fixed internal <density>.
The competition is visible in the scaling <free energy>
$$
\frac{F}{k_BT}\sim\frac{R^2}{Na^2}+\frac{vN^2}{R^3}+\frac{uN^3}{R^6},\qquad u>0.
$$
For $v>0$, elastic cost balances two-segment repulsion to give the swollen-coil law. At $v=0$, three-segment repulsion stabilizes ideal-chain scaling; for $v<0$, attraction balanced by the positive three-segment term gives $R^3\sim uN/|v|$. The dense <polymer globule> also has an interfacial <free energy>. The scaling expression explains regimes, not all fluctuation corrections or a detailed finite-chain transition curve. A finite chain crosses over smoothly; the sharp theta-point limit refers to indefinitely long chains.
A dilute-solution light-scattering experiment can follow <radius of gyration> while changing <temperature> or <solvent> composition. Measure at several concentrations and extrapolate toward isolated chains; check molecular-weight distribution, reversibility and the absence of growing multi-chain aggregates. <dynamic light scattering> measures <hydrodynamic size>, which is related to but distinct from <radius of gyration>. A falling scattering-derived size accompanied by a rising aggregate population cannot by itself establish single-chain collapse. \b[<solvent quality> controls conformation through the balance of segment interactions and <conformational entropy>.]
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